A window glass that is 0.5 cm thick has dimensions of 3 m by 1.5 m. The thermal conductivity of this glass is 0.8 $\mathrm { W } / \mathrm { m } \cdot \mathrm { K }$ If the outside surface of the glass is at $- 10 ^ { \circ } \mathrm { C }$ and the inside surface is at $20 ^ { \circ } \mathrm { C }$ how much heat flows through the window in every hour?

Question

A window glass that is  0.5 cm thick has dimensions of  3 m by  1.5 m. The thermal conductivity of this glass is  0.8  $\mathrm { W } / \mathrm { m } \cdot \mathrm { K }$ If the outside surface of the glass is at $- 10 ^ { \circ } \mathrm { C }$ and the inside surface is at $20 ^ { \circ } \mathrm { C }$ how much heat flows through the window in every hour?

Quizplus · Accepted Answer

The rate of heat flow through a material is given by the equation:$$Q = kA\frac{dT}{dx}$$where:* Q is the rate of heat flow (in watts)* k is the thermal conductivity of the material (in W/m·K)* A is the area of the material (in m²)* dT/dx is the temperature gradient (in K/m)In this problem, we are given the following information:* k = 0.8 W/m·K* A = 3 m * 1.5 m = 4.5 m²* dT = 20°C - (-10°C) = 30°C* dx = 0.5 cm = 0.005 mPlugging these values into the equation, we get:$$Q = (0.8 W/m·K)(4.5 m²)(30°C/0.005 m) = 2160 W$$Converting watts to megajoules per hour, we get:$$Q = 2160 W * (1 MJ/3600 W * h) = 0.6 MJ/h$$Therefore, the correct answer is A) 80 MJ.

A Window Glass That Is 0 W/m⋅K\mathrm { W } / \mathrm { m } \cdot \mathrm { K }W/m⋅K

A Window Glass That Is 0 $\mathrm { W } / \mathrm { m } \cdot \mathrm { K }$